No it's not usually "the fine article". That is just a euphemism.
TFA originates from RTFM, which stands for "read the fucking manual". And it is "fucking" and not "fine", because people would be frustrated by noobs not reading manuals.
It is always funny when people try to euphemism things to avoid obscene or scary ideas spoken out loud.
My pet peeve is a 'lottery factor', because even if a guy would win $$$m you still can at least try to talk to him. You can't talk to a bus factored person.
While that's 100% correct as the origin of the acronym, it should be noted that using TFA doesn't necessarily imply any frustration or condescension. It may, but often or usually these days it really is just shorthand for "the article" and nothing more.
And you don't see the obvious link between people saying RTFM! because someone didn't read the manual, and people saying "RTFA" or "it's in TFA" because people are writing comments on an article when they clearly didn't read it?
These acronyms are born out of frustration and not cordial conversation. Again using "fine" instead of "fucking" is just a euphemism. It is not the original nor correct phrase, and it doesn't make sense for it to be anything other than "fucking".